The diagonal of an isosceles trapezoid is the bisector of an acute angle, and the bases are 1: 2.
| August 31, 2021 | education
The diagonal of an isosceles trapezoid is the bisector of an acute angle, and the bases are 1: 2. the perimeter of the trapezoid is 90. Find the larger side of the trapezoid.
The perimeter of a trapezoid is equal to the sum of the lengths of its sides.
As already established, the lengths of the sides of the trapezoid are a, a, a and 2a.
P = a + a + a + 2a = 5a;
Therefore, the length of the smaller base of the trapezoid
a = P / 5 = 90/5 = 18.
The larger base of the trapezoid is twice the size of the smaller one:
2a = 18 * 2 = 36.
Answer: the length of the larger base of the trapezoid is 36.
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